L25_ Mohrs_Circle-fall 10

L25_ Mohrs_Circle-fall 10 - EAS 209-Fall 2010 Instructors:...

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EAS 209-Fall 2010 Instructors: Christine Human 11/1/2010 1 Lecture 25- Mohr’s Circle Lecture 25 Mohr’s Circle for Plane Stress Today’s Objectives: Use Mohr’s circle to: calculate stresses at any orientation determine magnitude and orientation of principle stresses etc. add stress states Today’s Homework: For additional help understanding Mohr’s circle see website below for animation http://web.mst.edu/~mecmovie/ EAS 209-Fall 2010 Instructors: Christine Human 11/1/2010 2 Lecture 25- Mohr’s Circle Mohr’s Circle is a graphical approach to finding the stress component at any orientation. Procedure was developed by a German engineer – Otto Mohr (1835-1918) Recall from last lecture that the stresses in the direction of the transformed axes can be combined to give the equation for a circle A plot of this circle gives a graphical view of the stresses in an element at any angle . A procedure to plot Mohr’s circle is given next:   2 2 2 2 2 2 2 where xy y x y x ave y x ave x R R 2 sin 2 cos 2 2 xy y x y x x 2 cos 2 sin 2 xy y x y x
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EAS 209-Fall 2010 Instructors: Christine Human 11/1/2010 3 Lecture 25- Mohr’s Circle STEP 1 : Determine the stresses σ x , σ y and τ xy . STEP 2: Draw a set of axes to the same scale STEP 3: Plot point X with coordinates ( σ x , - τ xy ) Plot point Y with coordinates ( σ y , τ xy ) Note that positive
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L25_ Mohrs_Circle-fall 10 - EAS 209-Fall 2010 Instructors:...

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